Hyperboloidal layers for hyperbolic equations on unbounded domains

• Published in: Journal of computational physics Vol. 230; no. 6; pp. 2286 - 2302
• Main Author: ZENGINOGLU, Anil
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.03.2011; Elsevier
• Subjects: Boundaries; Computational techniques; Exact sciences and technology; Hyperboloidal compactification; Hyperboloidal layers; Ingredients; Mathematical analysis; Mathematical methods in physics; Mathematical models; Maxwell equation; Maxwell equations; Nonlinearity; Perfectly matched layers; Physics; Spectra; Transformations; Transparent (non reflecting, absorbing) boundary conditions; Wave equations; Hyperboloidal compactification; Perfectly matched layers; Hyperboloidal layers; Maxwell equations; Transparent (non reflecting, absorbing) boundary conditions; Wave equations; Compactification; Hyperbolic equations; Calculation; Absorbing boundary condition; Calculation methods
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.12.016

We show how to solve hyperbolic equations numerically on unbounded domains by compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate in combination with spatial compactification. We construct a new layer method based on this idea, called the hyperboloidal layer. The method is demonstrated on numerical tests including the one dimensional Maxwell equations using finite differences and the three dimensional wave equation with and without nonlinear source terms using spectral techniques.